Contou-Carrère symbol, Deligne pairing and quintets

We prove the reciprocity laws for a family of projective curves over an affine base scheme, where curves can be singular and reducible, and the base can be non-Noetherian. These reciprocity laws generalize the Weil reciprocity law for a projective curve over a field and the reciprocity law for the Contou-Carr\`ere symbol. We apply the proven reciprocity laws to describe the actions of certain central extensions of the group ind-scheme related with the formal punctured disc on certain line bundles on the moduli stacks of quintets. A quintet consists of a geometric data on a family of curves including a line bundle on this family. The line bundles on the moduli stacks are constructed using the Deligne pairings of line bundles from quintets.